login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284391 1-limiting word of the morphism 0 -> 1, 1 -> 001. 4
1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

The morphism 0 -> 1, 1 -> 001 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 1 -> 001 -> 11001 -> 00100111001; if the number of iterations is odd, the 1-word evolves from 0 -> 1 -> 001 -> 11001 -> 00100111001 -> 110011100100100111001, as in A284391. The 0-limiting word results from the 1 limiting word by replacing the initial 00 by 1.

Conjecture: the limiting frequency of 0's in both limiting words is 1/2.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {0, 0, 1}}] &, {0}, 9]; (* A284391 *)

Flatten[Position[s, 0]];  (* A284392 *)

Flatten[Position[s, 1]];  (* A284393 *)

CROSSREFS

A284388 shifted right. Cf. A284392, A284393.

Sequence in context: A267869 A068434 A323511 * A127015 A281114 A286749

Adjacent sequences:  A284388 A284389 A284390 * A284392 A284393 A284394

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 30 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 17:33 EDT 2021. Contains 345085 sequences. (Running on oeis4.)